One trillionth is the reciprocal of a trillion, which means it has one of two definitions depending on whether the long scale or short scale numbering system is in use.
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Short scale countries
In most English-speaking countries, a trillionth is equal to 0.000 000 000 001, or 1 x 10−12 in scientific notation. The prefix for a number of this magnitude is pico (pronounced "peeko"), and is abbreviated as lowercase p.
Long scale countries
In most European countries, a trillionth is equal to 0.000 000 000 000 000 001, or 1 x 10−18 in scientific notation. The prefix for a number of this magnitude is atto, and is abbreviated as lowercase a.
References
Trillionth Wikipedia(Text) CC BY-SA